A379482 a(n) = sigma(A003961(n^2)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.

1, 13, 31, 121, 57, 403, 133, 1093, 781, 741, 183, 3751, 307, 1729, 1767, 9841, 381, 10153, 553, 6897, 4123, 2379, 871, 33883, 2801, 3991, 19531, 16093, 993, 22971, 1407, 88573, 5673, 4953, 7581, 94501, 1723, 7189, 9517, 62301, 1893, 53599, 2257, 22143, 44517, 11323, 2863, 305071, 16105, 36413, 11811, 37147, 3541

Offset: 1

Author

Antti Karttunen, Dec 27 2024

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to prime indices in the factorization of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000290, A003973, A048673, A151800, A378231, A379223, A379481, A379483, A379484 [= A038500(a(n))].

Cf. also A337336, A337337.

Programs

Mathematica

{1}~Join~Array[DivisorSigma[1, #] &[Apply[Times, Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]] ]^2] &, 52, 2] (* Michael De Vlieger, Dec 27 2024 *)

PARI

A379482(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1); f[i, 2] *= 2); sigma(factorback(f)); };

Formula

Multiplicative with a(p^e) = (q^(2e+1) - 1)/(q-1), where q = nextprime(p) = A151800(p).

a(n) = A000203(A379481(n)) = A003973(A000290(n)).

a(n) = A379223(A048673(n)).

a(n) = 2*A379481(n) - A378231(n).